Problem: $\dfrac{d}{dx}\left(x^{-8}\right)=$
Explanation: The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a negative number.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{-8}\right) \\\\ &=-8x^{-8-1} \gray{\text{The power rule}} \\\\ &=-8x^{-9} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{-8}\right)=-8x^{-9}$. This can also be written as $-\dfrac{8}{x^9}$ (all equivalent forms are accepted).